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Basic Proportionality Theorem (Thales Theorem) Video Lecture - Class 10

FAQs on Basic Proportionality Theorem (Thales Theorem) Video Lecture - Class 10

1. What is the Basic Proportionality Theorem?

Ans. The Basic Proportionality Theorem, also known as Thales' Theorem, states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. In other words, if a line is drawn parallel to one side of a triangle, it intersects the other two sides in such a way that the ratios of the corresponding segments are equal.

2. How can the Basic Proportionality Theorem be applied?

Ans. The Basic Proportionality Theorem can be applied in various geometric situations. It can be used to find unknown side lengths or to prove that certain lines are parallel. By using the theorem, we can set up proportions and solve for the unknown variables.

3. Can the Basic Proportionality Theorem be used in non-right angled triangles?

Ans. Yes, the Basic Proportionality Theorem can be used in non-right angled triangles as well. The theorem holds true for all types of triangles, not just right angled ones. As long as a line is drawn parallel to one side of a triangle, it will divide the other two sides proportionally.

4. Are there any other theorems related to the Basic Proportionality Theorem?

Ans. Yes, there are several theorems related to the Basic Proportionality Theorem. Some of them include the Converse of the Basic Proportionality Theorem, which states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side. Another related theorem is the Midpoint Theorem, which states that if a line passes through the midpoint of one side of a triangle and is parallel to another side, it divides the third side into two equal segments.

5. How can the Basic Proportionality Theorem be used to solve real-world problems?

Ans. The Basic Proportionality Theorem can be applied to solve various real-world problems involving similar triangles. For example, it can be used to determine the height of a building or a tree by measuring shadows and using proportions. It can also be used in engineering and architecture to ensure that structures are built with correct proportions and dimensions. By understanding and applying this theorem, we can solve practical problems related to scaling, measurement, and design.

Text Transcript from Video

basic proportionality theorem the
theorem states that a line parallel to
one side of a triangle divides the other
two sides proportionally triangle ABC
has a line drawn parallel to BC which
cuts a B and AC at points P and Q
respectively we are required to prove
that AP by PB is equal to aq by QC
construction let Point P divided a B in
the ratio of L is 2 m where L and M are
natural numbers divide a P in L and PV
in M equal parts click on go for the
proof of the theorem
a pea is cut into L equal parts and
lines are drawn through these points
parallel to BC which is nothing but the
construction
therefore a Q is also cut into L equal
parts we know this from the intercept
theorem
similarly QC is cut into m equal parts
AP by PB is equal to L by M since P
divides a B in the ratio L is 2 m
therefore a Q by Q C is equal to L by M
therefore AP by P B is equal to a Q by Q
C thus the basic proportionality theorem
is proved

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Oct 14, 2025 Last updated

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